In: Statistics and Probability
In 2010, the U.S. population was about 309 million. The overall
birth rate was 13.0 births per 1000, and the overall death rate was
7.4 deaths per 1000.
a) Approximately how many births were there in the United
States?
b) About how many deaths were there in the United States?
c) Based on births and deaths alone (not counting immigration or
emigration), about how much did the U.S. population increase during
2010?
d) Suppose that during 2010 the U.S. population actually increase
by 3.5 million. Based on this fact and your results from part (c),
estimate how many people immigrated to the United States. What
proportion of the overall population growth was due to
immigration?
Answer)
a) It is mentioned in the question that, the birth rate is 13/1000
that is 13 births per 1000 people
so first we will convert the 309 million(present population into 1000)
as there are 1000000 in one million
so in 309 million, there are 1000000*309 thousand
= 309000000
so we have 309000 * 1000
as there are 13 births per 1000
so there will be 13*309000 births per 309000000
= 4017000
b)
7.4 deaths per 1000
that is 7.4 deaths per 1000
so first we will convert the 309 million(present population into 1000)
as there are 1000000 in one million
so in 309 million, there are 1000000*309 thousand
= 309000000
so we have 309000 * 1000
so
7.4*309000 deaths per 309000*1000 or 309 million
= 2286600
c)
total population = 309000000
total number of births = 4017000
so total population now = 309000000 + 4017000
now we need to subtract the total number of deaths in order to find the present population
total number of deaths = 2286600
present population = 309000000 + 4017000 - 2286600
310730400
d)
as us population actually increased by 3.5 million
so 309 + 3.5 = 312.5 million
or converting it into thousands = 312.5*1000000 = 312500000
this is the actual population
but in part c we calculated 310730400 (not counting immigration or emigration)
so the total number of immigrants = 312500000 - 310730400
= 1769600
and total population growth is 3.5 million or 3500000
so the proportion of the overall population growth due to immigration = 1769600/3500000
= 0.5056